If you have heard
anything about stirred yeast starters you've probably heard that stir plates produce
more yeast than starters that are not agitated.
This seems to be a misconception that has been unfortunately widely propagated.
I'm sure Jamil
had the best intentions when
creating his Mr. Malty Starter Calculator, however it seems that brewers have
taken the results out of context and drawn conclusions from the calculator that
I doubt Jamil intend.
The data behind
the vastly popular Mr. Malty equation are from growth that had no aeration and
(Details of this
experiment can be found in the widely acclaimed book: Yeast by Dr. Chris White
and Jamil Zainasheff. 
If you haven't
read this book I highly recommend you get a copy.)
There is an anecdotal reference to increased
yield from agitation in the book Yeast, however without more detail on how the yield was
compared we can only guess as to what the author observed.
It is also common in scientific papers to use
"specific growth rate" (a measure of the speed of propagation)
interchangeable with yield.
Without further explanation I can only assume
this is what Dr. Chris White may be refereeing to.
The lack of aeration make Chris White's experiments questionable when used to predict growth on a
stir plate. Oxygen is critical for
sterol production in yeast. Without
aeration an the onset of fermentation the yeast membranes will lack the
pliability they need to bud new cells.
Given proper aeration at inoculation yeast can double four times,
growing to sixteen times the initial population.  Without aeration, as was done by Chris White
for the experiments that Jamil used for his calculator, the data show that cell
budding was extremely limited. This limitation follows what may be expected given the volume of dissolved oxygen.
Stir plates produce
yeast faster, but do not produce more yeast.
In scientific papers
on yeast propagation you will generally see that the time frame used is 48
hours.  Propagation occurs much more rapidly with a
stir plate so at the 48 hour mark there is often substantially more yeast
produced with some form of agitation.
However, given enough time, without agitation a similar amount of yeast
is produced. 
Yeast can metabolize
sugar much more efficiently in the presence of oxygen aerobically than without
anaerobically.  Using a stir plate oxygen is constantly
introduced. The common conclusion from
these two facts is that with a stir plate considerably more sugar will be
metabolized aerobically than without.
This is, however, not the case due to the Crab Tree Effect. When the sugar concentration is typically
above 0.5% w/w (0.5°P or 1.002 SG) yeast will metabolize sugar using
anaerobic fermentation. The balance
between aerobic respiration and anaerobic fermentation is similar independent
 J. Novak, G.
Basarova, J. A. Teixeira and A. A. Vicente,
Brewing Yeast Propagation Under Aerobic and Anaerobic Conditions Employing Flow
Cytometry. J. Inst. Brew. 113(3), 249–255, 2007
 Greg Doss, Yeast Propagation A Practical Approach
 L. Camacho-Ruiz, N. Pérez-Guerra, R. Pérez Roses, FACTORS AFFECTING THE GROWTH OF SACCHAROMYCES CEREVISIAE IN BATCH CULTURE AND IN SOLID SATE FERMENTATION
 C. R. Murray, T. Barich and D. Taylor, The Effect of Yeast Storage Conditions on Subsequent Fermentations,
 R. H. DE DEKEN, The Crabtree Effect: A Regulatory System in Yeast